We introduce the concept of Baire embeddings and we classify them up to C conjugacies. We show that two such embeddings are Cequivalent if and only if they have exponentially equivalent geometries. Next, we introduce the class of IFS-like Baire embeddings and we also show that two Hölder equivalent IFS-like Baire embeddings are C conjugate if and only if their scaling functions are the same. In...

We prove: (1) Every Baire measure on the Kojman-Shelah Dowker space [10] admits a Borel extension. (2) If the continuum is not a real-valued measurable cardinal then every Baire measure on the M. E. Rudin Dowker space [16] admits a Borel extension. Consequently, Balogh’s space [3] remains as the only candidate to be a ZFC counterexample to the measure extension problem of the three presently kn...

We study continuous descent methods for minimizing convex functions defined on general Banach spaces and prove that most of them (in the sense of Baire category) converge.

We establish some results on the Wadge degrees and on the Boolean hierarchy of k-partitions of some spaces, where k is a natural number. The main attention is paid to the Baire space, Baire domain and their close relatives. For the case of Δ2-measurable k-partitions the structures of Wadge degrees are characterized completely. For many degree structures, undecidability of the first-order theori...

Let κ be a regular cardinal. Consider the Baire numbers of the spaces (2)κ for various θ ≥ κ. Let l be the number of such different Baire numbers. Models of set theory with l = 1 or l = 2 are known and it is also known that l is finite. We show here that if κ > ω, then l could be any given finite number. The Baire number of a topological space with no isolated points is the minimal cardinality ...

 In Proposition 2.6 in (G‎. ‎Gruenhage‎, ‎A‎. ‎Lutzer‎, ‎Baire and Volterra spaces‎, ‎textit{Proc‎. ‎Amer‎. ‎Math‎. ‎Soc.} {128} (2000)‎, ‎no‎. ‎10‎, ‎3115--3124) a condition that‎ ‎every point of $D$ is $G_delta$ in $X$ was overlooked‎. ‎So we‎ ‎proved some conditions by which a Baire space is equivalent to a‎ ‎Volterra space‎. ‎In this note we show that if $X$ is a‎ ‎monotonically normal $T_1...

We show that small-bound isomorphisms of spaces affine continuous functions on Choquet simplices with Lindel?f boundaries induce Baire measurable bijections their sets extreme points.

$C_{p}\left ( X\right )$ is distinguished $\Leftrightarrow$ the strong dual $L_{\beta }\left barrelled bidual $M\left ) =\mathbb {R}^{X}$. So one may judge how nearly by is, and also near dense subspace to Baire space $\mathbb Being Baire-like, always fairly close {R}^{X}$ in that sense. But if not distinguished, we show codimension of uncountable, i.e., algebraically far from {R}^{X}$, moreove...

This paper introduces the concepts of fuzzy pseudo-open sets in fuzzy topological spaces and fuzzy pseudo-continuous functions between fuzzy topological spaces. Several characterizations of fuzzy pseudo-open sets are established. A conditions under which fuzzy hyper-connected spaces become fuzzy Baire spaces, is obtained by means of fuzzy pseudo-open sets. Several examples are given to illustra...